Generalized Function-on-Function Regression

• Activity Number: 528
• Type: Topic Contributed
• Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
• Sponsor: International Indian Statistical Association
• Author(s): Janet S. Kim* and Ana-Maria Staicu and Arnab Maity
• Companies: North Carolina State University and North Carolina State University and North Carolina State University
• Keywords: Bootstrap ; Functional regression ; Generalized function-on-function regression ; Orthogonal projection ; Penalized B-splines ; Prediction

Abstract

We consider non-linear regression models for functional responses and functional predictors observed on possible different domains. We introduce a flexible model that relates the value of response variable at a particular time point to the entire profile of the covariate as well as the time point of the response. There are two innovations in this paper. First, we develop an effective estimation procedure that reduces the dimension of model parameters by orthogonal projection of the functional response. Second, we develop an inferential procedure that accounts for uncertainty in error process as well as uncertainty in functional principal component (FPC) decomposition. The proposed estimation/inferential procedure accommodates various realistic settings such as correlated error structure as well as sparse and/or irregular design. We investigate our methodology in finite sample size through simulations and a real data application.